Analysis of mean and mean square response of general linear stochastic finite element systems

Papadopoulos, Vissarion; Papadrakakis, Manolis; Deodatis, George

doi:10.1016/j.cma.2005.11.008

Cited by 31 publications

(31 citation statements)

References 11 publications

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“…Certainly, the probability theory is the most popular tool for FE analyses under uncertainties. For instance, Papadopoulos et al [1] presented a FE-based analysis of the mean and of the mean square response for stochastic structural systems whose material properties are described by using the random field technique. 0045 The classical stochastic FE analysis is based on series expansion (e.g., Taylor expansion, perturbation technique or Neumann expansion) of the involved stochastic mathematical items with respect to the stochastic parameters of the problem [2].…”

Section: Finite Element Methods Under Probabilistic Uncertaintiesmentioning

confidence: 99%

Finite element analysis with uncertain probabilities

Quaranta

2011

Computer Methods in Applied Mechanics and Engineering

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Section: Finite Element Methods Under Probabilistic Uncertaintiesmentioning

confidence: 99%

Finite element analysis with uncertain probabilities

Quaranta

2011

Computer Methods in Applied Mechanics and Engineering

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“…; i D 1; : : : ; n dof (24) where n dof is the total number of degrees of freedom. (4) Steps 1-3 are repeated for different values of the wave number Ä of the random sinusoid.…”

Section: Fast Monte Carlo Simulationmentioning

confidence: 99%

“…Recent advances include extension of this approach to nonlinear and/or dynamic problems . Different aspects and applications of the VRF were introduced in , while an efficient fast Monte Carlo simulation for the numerical computation of VRF of this approach was provided in . A development of this approach, which further boosted the validity of the assumption of independence of VRF to the stochastic parameters of the problem, was proposed in where the concept of generalized VRF was introduced, which is derived from a family of different VRFs for corresponding combinations of different PDFs with different sets of power spectral density functions.…”

Section: Introductionmentioning

confidence: 99%

An adaptive spectral Galerkin stochastic finite element method using variability response functions

Giovanis

Papadopoulos

Stavroulakis

2015

Numerical Meth Engineering

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SUMMARYA methodology is proposed in this paper to construct an adaptive sparse polynomial chaos (PC) expansion of the response of stochastic systems whose input parameters are independent random variables modeled as random fields. The proposed methodology utilizes the concept of variability response function in order to compute an a priori low-cost estimate of the spatial distribution of the second-order error of the response, as a function of the number of terms used in the truncated Karhunen-Loève (KL) expansion. This way the influence of the response variance to the spectral content (correlation structure) of the random input is taken into account through a spatial variation of the truncated KL terms. The criterion for selecting the number of KL terms at different parts of the structure is the uniformity of the spatial distribution of the second-order error. This way a significantly reduced number of PC coefficients, with respect to classical PC expansion, is required in order to reach a uniformly distributed target second-order error. This results in an increase of sparsity of the coefficient matrix of the corresponding linear system of equations leading to an enhancement of the computational efficiency of the spectral stochastic finite element method.

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“…Many studies have contributed to the development of this field. These studies include investigations on the vibration and reliability of stochastical turbine blades [11,12], response analysis of stochastic structural systems [13,14], eigenvalue problem of stochastic structures [15,16], and so on [17][18][19][20]. However, except for the work of Sankar et al [21], rotor system stochasticity problems have not received substantial attention.…”

Section: Introductionmentioning

confidence: 98%

Stochastic finite element modeling and response analysis of rotor systems with random properties under random loads

2015

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Random properties and random loads are highly important in rotor dynamic analysis because they cause system dynamic responses to behave randomly. In this paper, a stochastical finite element of rotating shaft based on Timosheko beam theory is proposed for rotor system modeling, in which material and geometric random properties are considered one-dimensional stochastic field functions. A random response analytical method is developed to determine the statistics of the dynamic responses of stochastical rotor systems under random loads. The numerically obtained whirl speed of a turbopump rotor system is compared with the test data to validate the proposed model, and good agreement is observed. Linear and nonlinear turbopump rotor systems are employed to compare the results obtained from the proposed model and the Monte Carlo simulation. The numerically predicted results, which coincide well with Monte Carlo simulation data, demonstrate the feasibility and efficiency of the proposed stochastic model and method for actual rotor system analysis and design.

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Analysis of mean and mean square response of general linear stochastic finite element systems

Cited by 31 publications

References 11 publications

Finite element analysis with uncertain probabilities

Finite element analysis with uncertain probabilities

An adaptive spectral Galerkin stochastic finite element method using variability response functions

Stochastic finite element modeling and response analysis of rotor systems with random properties under random loads

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